Prediction Intervals of Small-Area Means Under Semiparametric Measurement Error Models

• Activity Number: 634
• Type: Topic Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Survey Research Methods Section
• Author(s): Gauri S. Datta* and Aurore Delaigle and Peter Hall and Lily Wang
• Companies: University of Georgia/U.S. Census Bureau and The University of Melbourne and The University of Melbourne and Iowa State University
• Keywords: Area-level model ; Fay-Herriot model ; Structural measurement error

Abstract

Demand for reliable estimates for characteristics of small areas has considerably increased worldwide due to a growing use of such estimates in formulating national policies and programs, allocating government funds, planning regional development, and making decisions at the local level. However, cost and operational considerations rarely make it possible to get a large enough sample at the small area level to support direct estimates with adequate precision for all domains of interest. Model-based methods are used to produce reliable estimates. We consider an adaptation of the Fay-Herriot model for the area-level data where one covariate is measured with error. We consider structural measurement error model and a semi-parametric approach to produce accurate prediction intervals for small area means. We replace the normality assumption of the sampling error and the normality assumption of the measurement error of a covariate by heavy-tailed distributions. Estimating the unknown measurement error density nonparametrically, we develop both point estimates and prediction intervals of small area means. We present an expansion of the coverage error of the proposed prediction intervals.